Direct adaptive control of nonlinear systems via implicit function emulation

Abstract

We consider the direct adaptive control of a general nonlinear dynamical system with only weak assumptions about the order and relative degree of the plant. The plant may be nonlinear in the control, and only output feedback is required. The underlying idea is to adaptively emulate the implicit function of the unknown dynamical relationship between the input and output of the system. If a linearly parameterized model (in particular, a radial gaussian network) is used for this purpose, we show that the adaptation process converges and, in turn, gives rise to bounded output tracking error, if a network with a sufficiently large number of nodes is used.